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Continuum approaches are computationally tractable, but limited in applicability due to built-in modeling assumptions; e.g., models suitable for granular flows typically fail to capture clogging, bouncing and ballistic motion. In our hybrid approach, an oracle dynamically partitions the domain into continuum regions where safe, and discrete regions where necessary. The domains overlap along transition zones, where a Lagrangian dynamics mass-splitting coupling principle enforces agreement between the two simulation states. Enrichment and homogenization operations allow the partitions to evolve over time. This approach accurately and efficiently simulates scenarios that previously required an entirely discrete treatment.<\/jats:p>","DOI":"10.1145\/3272127.3275095","type":"journal-article","created":{"date-parts":[[2018,11,28]],"date-time":"2018-11-28T19:16:10Z","timestamp":1543432570000},"page":"1-19","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":78,"title":["Hybrid grains"],"prefix":"10.1145","volume":"37","author":[{"given":"Yonghao","family":"Yue","sequence":"first","affiliation":[{"name":"The University of Tokyo, Columbia University"}]},{"given":"Breannan","family":"Smith","sequence":"additional","affiliation":[{"name":"Columbia University"}]},{"given":"Peter Yichen","family":"Chen","sequence":"additional","affiliation":[{"name":"Columbia University"}]},{"given":"Maytee","family":"Chantharayukhonthorn","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology"}]},{"given":"Ken","family":"Kamrin","sequence":"additional","affiliation":[{"name":"Massachusetts Institute of Technology"}]},{"given":"Eitan","family":"Grinspun","sequence":"additional","affiliation":[{"name":"Columbia University"}]}],"member":"320","published-online":{"date-parts":[[2018,12,4]]},"reference":[{"key":"e_1_2_2_1_1","volume-title":"Numerical Methods for Nonsmooth Dynamical Systems: Applications in Mechanics and Electronics","author":"Acary Vincent","unstructured":"Vincent Acary and Bernard Brogliato . 2008. 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In Bifurcation and Degradation of Geomaterials in the New Millennium. Springer, 161--167."},{"key":"e_1_2_2_83_1","doi-asserted-by":"publisher","DOI":"10.5555\/946250.946949"},{"key":"e_1_2_2_84_1","volume-title":"Martinez-Dura","author":"Pla-Castells Marta","year":"2008","unstructured":"Marta Pla-Castells , Ignacio Garc\u00eda-Fernandez , and Rafael J . Martinez-Dura . 2008 . Physically-Based Interactive Sand Simulation. In Eurographics 2008 - Short Papers . Marta Pla-Castells, Ignacio Garc\u00eda-Fernandez, and Rafael J. Martinez-Dura. 2008. Physically-Based Interactive Sand Simulation. In Eurographics 2008 - Short Papers."},{"key":"e_1_2_2_85_1","volume-title":"Computational Granular Dynamics: Models and Algorithms","author":"P\u00f6schel Thorsten","unstructured":"Thorsten P\u00f6schel and Thomas Schwager . 2005. Computational Granular Dynamics: Models and Algorithms . Springer Science & Business Media . Thorsten P\u00f6schel and Thomas Schwager. 2005. 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